It seems a little weird, but maybe I'm missing something.
Lydia is my current companion and won't "naturally" follow me into the temple. I went back outside to check, and yep -- she's standing right by the door.
I have tried to help her to enter by issuing a direct command but she tells me can't. (I haven't tested whether this works in general, though.)
Is this a glitch or a gameplay element -- maybe the 'arcane/evil' factor of the place combined with my 'unmagic' follower or something?